These lectures were given at the * MITP Summer School 2018: Towards
the Next Effective Quantum Field Theory of
Nature*. They provide a first introduction to effective field
theory, illustrating the basic concepts with concrete examples,
mostly from QED.

Basic terminology, steps in the construction of an effective theory

Operator dimension

Why effective theories?

QED at very low energy: the Euler-Heisenberg Lagrangian

Equation-of-motion operators

Matching, photon-photon scattering at low energies

Power counting and loop corrections

Fermi theory for charged-current quark decay

Renormalization and operator mixing, renormalization group (RG)

Resummation by RG evolution: RG improved perturbation theory

Soft Effective Theory: soft photons in electron-electron scattering

Expansion of loop integrals and the method of regions

Thomas Becher